Heavy duty radial tire carcass profile

ABSTRACT

A heavy duty radial tire includes at least one radial carcass extending from one bead portion to the other bead portion and using inextensible cords and a belt arranged outwardly of the radial carcass for reinforcing a tread of the tire. The tire comprises, during expanding of the tire from 5% to 100% of a normal inner pressure, a first profile portion expanding radially outwardly in a tread zone, a second profile portion depressing axially inwardly of the tire in a radially outer zone of a sidewall from one end of said tread to a tire maximum width position when filled with the normal inner pressure, and a third profile portion expanding axially outwardly of the tire in a radially inner zone of the sidewall from the tire maximum width position when filled with the normal inner pressure to a parting point of the sidewall from the rim, thereby properly distributing strains occurring in the tire in filling with the normal inner pressure.

This is a continuation of application Ser. No. 07/595,726 filed Oct. 3,1990, now abandoned, which was a continuation of application Ser. No.07/433,942 filed on Nov. 9, 1989, now abandoned, which in turn was acontinuation of application Ser. No. 07/118,127 filed on Nov. 9, 1987and is now U.S. Pat. No. 4,915,151.

BACKGROUND OF THE INVENTION

This invention relates to a pneumatic radial tire and more particularlyto a heavy duty radial tire for trucks or buses, whose durability isimproved by preventing separations occurring at ends of a belt forreinforcing a tread and at ends of carcass plies for principallyreinforcing the tire.

In order to improve the durability of bead portions of pneumatic radialtires, techniques of turn up of carcass plies and materials andconstructions of chafers or stiffeners as reinforcements have beengenerally investigated. However, with all proposed solutions,applications are limited to tires of some particular sizes although theyare relatively effective for tires of some limited sizes. Moreover,proposed solutions sometimes tend to increase costs of tires. Therefore,a fundamental solution has not been provided yet.

In order to obtain required performances of tires, in general, carcassconfigurations have been determined so as to expand uniformly whenfilled with inner pressure. The equilibrium configuration curve of acarcass line of a tire has been used in this industrial field, which isbased on the so-called "natural equilibrium theory" assuming thatcarcass cords are not extensible and deformations of the tire are notaffected by inner pressures. A carcasses of such a tire is uniformlysubjected to tensile forces and therefore its various performances aregood. However, such a tire is a theoretical one which could not exist infact. It is considered that an actual tire which approximates to such atheoretical tire as much as possible can be obtained by making theactual tire which uniformly inflates or is similar in figure before andafter the inflation. An actual tire obtained in this manner has a"natural equilibrium shape" of a carcass. In the following publicationsdisclosed hitherto measures for controlling the change in shape of tireswhen they are filled with inner pressure have been employed.

In U.S. Pat. No. 4,155,392, when a tire is being filled with innerpressure, maximum width portions of the tire are displaced radiallyinwardly to reduce tensile strains occurring in sidewalls, therebyimproving the durability of the life of the tire referring to FIG. 3 ofthe U.S. Pat. No. 4,155,392. In this case, however, parts of a tread andshoulders are also moved axially and radially inwardly to reduce initialtensions acting upon a belt of the tire so that moving performances ofthe tire and durability at ends of the belt are detrimentally affected.

U.S. Pat. No. 4,481,994 discloses a technique similar to the measuredisclosed in the above United States Patent specification. In this case,portions extending from ends of a belt to shoulders are also movedaxially and radially inwardly of a tire when filling normal pressure. Asa result, initial tensions of the belt become small which detrimentallyaffect various performances of the tire.

Moreover, U.S. Pat. No. 4,513,802 discloses a feature of changing a tireconfiguration to reduce the rolling resistance of a tire. In this case,however, as radially outward portions of sidewalls outwardly expand whenfilling normal inner pressure, expanding deformations are insufficientin bead portions and tread portion. Therefore, strain distributions inthe tire resulting from the expanding deformations are improper andtherefore sufficient durability for heavy duty tires is not obtained.

SUMMARY OF THE INVENTION

It is a principal object of the invention to provide a heavy dutypneumatic tire whose durability at bead and belt portions is effectivelyimproved without detrimentally affecting other portions of the tire.

In order to accomplish this object, in a heavy duty radial tireincluding at least one radial carcass extending from one bead portion tothe other bead portion and using inextensible cords and a belt arrangedoutwardly of the radial carcass for reinforcing a tread of the tireaccording to the invention, the improvement comprises an outer profileof the tire in radial cross-sections mounted on an approved rim whosewidth is not wider than that of a design rim and under no load conditionduring filling inner pressure from 5% to 100% of a normal innerpressure, said outer profile of the tire comprising a first profileportion expanding radially outwardly in a tread zone from one end ofsaid tread through a crown center to the other end of said tread, asecond profile portion depressing axially inwardly of the tire at leastin a part of a radially outer zone of a sidewall from said one end ofsaid tread to a tire maximum width position when filled with the normalinner pressure, and a third profile portion expanding axially outwardlyof the tire in a radially inner zone of said sidewall from said tiremaximum width position when filled with the normal inner pressure to aparting point of the sidewall from said rim, thereby properlydistributing strains occurring in the tire in filling with the normalinner pressure.

The invention by which a useful improvement of the heavy duty radialtire is accomplished resides in the discovery that strain distributionsin the tire suitable for improving the durability of the tire can beobtained by a novel and excellent measure for controlling the change inconfiguration of the tire when it is filled with inner pressure.

In order that the invention may be more clearly understood, preferredembodiments will be described, by way of example, with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a radial cross-section illustrating one fourth of a heavy dutyradial tire using a 5° flat base rim according to the invention;

FIG. 2 is a radial cross-section illustrating one fourth of a heavy dutyradial tire using a 15° drop center rim according to the invention;

FIGS. 3 and 4 are radial cross-sections of tires of naturallyequilibrium configuration of the prior art using 5° flat base and 15°drop center rims, respectively;

FIGS. 5 and 6 are radial cross-sections for explaining the naturallyequilibrium configuration of the tire.

FIGS. 7 and 8 are radial cross-sections of tires of naturallyequilibrium configuration;

FIGS. 9 and 10 are radial cross-sections of preferred embodiments oftires according to the invention;

FIGS. 11 and 12 are radial cross-sections of tires of the prior art;

FIGS. 13 and 14 are radial cross-sections of other embodiments of tiresaccording to the invention;

FIGS. 15 and 16 are radial cross-sections of tires of the prior art;

FIG. 17 is a schematic sectional view of a tire for explaining anadvantage of the tire according to the invention;

FIG. 18 is a schematic view of a tire for explaining another advantageof the tire according to the invention; and

FIG. 19 is a graph illustrating belt tensions in the tire according tothe invention and a tire of the prior art.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 1 and 2 illustrate heavy duty radial tires of different sizesaccording to the invention. In each drawing, solid lines illustratecarcass path lines 1 and a tire profile 2 determined thereby in a radialcross-section under a standard status when the tire mounted on a rim isfilled with an inner pressure 5% of a normal inner pressure. A belt on acarcass for reinforcing a tread is arranged in lamination embedded in atread of the tire substantially over an overall width of the tread insubstantially the same manner as in tires of the prior art although thebelt is not shown in order to avoid a complication caused bydeformations of the tire.

The standard status of a tire is defined herein by the change inconfiguration or the condition when filled with the slight pressure forreason that it is necessary for the present invention to keepconfigurations of the tire and carcass in any radial cross-sections whenthe tire formed and vulcanized in a mold is mounted on a design rimamong approved rims with a narrowed distance between beads of the tireor a rim having a width not wider than that of the design rim.

In case that a tire is difficult to fit on a rim or a tire isconsiderably deformed due to piled or stored conditions, after the tireis filled with normal inner pressure and kept for more than twenty fourhours, the inner pressure is exhausted to 5% of the normal innerpressure. When carcass deformations of tires are extreme due to storedconditions, the inner pressure is exhausted to 5% of the normal innerpressure after removing particularly deformed shapes by running ofseveral tens km. In this manner, a precise standard shape of the tire isobtained. The status of the tire at this moment, which keepsconfigurations of the tire and the carcass can be used a standardstatus.

In FIGS. 1 and 2, solid lines illustrate carcass path lines 1 and 2 when5% of normal inner pressure is filled and broken lines illustratecarcass path lines 1' and tire profiles 2' when normal inner pressure isfilled. The distinctive feature of the deformed tire configurationaccording to the invention is clearly evident from these solid lines 1and 2 and broken lines 1' and 2'. It is clearer in comparison with FIG.3 illustrating a deformed status of a comparison tire formed inso-called "natural equilibrium configuration" according to the priorart.

According to the invention, a substantially uniform expansion g occursradially outwardly of the tire on a tread 5 from one end 4 of a groundcontact surface through a tread center 3 to the other end (not shown) ofthe ground contact surface, while a depression d occurs axially inwardlyof the tire over at least part of a radially outer zone 7 of a sidewallfrom the end 4 of the ground contact surface to a tire maximum widthposition 6 after filled with the normal inner pressure. Moreover, anexpansion f occurs axially outwardly of the tire over a radially innerzone of the sidewall from the tire maximum width position 6 to a point 8where the sidewall leaves a rim flange or a parting point of thesidewall from the rim flange.

As can be seen from the drawings, we now consider one half of a tire.For example, therefore, we mentioned the sidewall as single although onetire includes two sidewalls.

There are the outward expansions at the tread portion 5 and the radiallyinner zone of the sidewall and the inward depression at the radiallyouter zone 7 in this manner when the tire is filled with the normalinner pressure according to the invention. The particular change inconfiguration according to the invention is accomplished by utilizingthe following general properties:

(1) The tire tends to expand as a whole,

(2) The carcass configuration tends to approach a natural equilibriumconfiguration,

(3) If substantially inextensible cords are used for carcass cord, thecarcass does not extend very well, and

(4) The deformations of the carcass by the filling of the inner pressureare caused as a chain reaction. A deformation does not occur in only onepart.

In this manner, the carcass line of the tire mounted on a rim and filledwith the inner pressure 5% of the normal inner pressure is located inthe tread portion 5 inside the carcass line or the equilibriumconfiguration curve of the tire filled with the normal inner pressure.The carcass line in the radially outer zone 7 of the sidewall has alarger curvature than that of the carcass line of the equilibriumconfiguration curve and located outside the carcass line of thenaturally equilibrium configuration of the tire when filled with thenormal inner pressure. Moreover, the carcass line from the radiallyinward zone 9 of the sidewall to the bead portion is locatedconsiderably inside the carcass line of the equilibrium configurationcurve of the tire when filled with the normal inner pressure. Further,substantially inextensible cords such as steel cords and aromaticpolyamide cords are used for the carcass plies so that when filled withthe normal inner pressure, the carcass line is inwardly depressed in theradially outer zone of the sidewall and in connection therewith isgreatly expanded outwardly in the crown portion and the radially innerzone.

For example, in case that the radially outer zone of the sidewall issimilar to the naturally equilibrium configuration, the carcass in thiszone is expanded or substantially not deformed so that the expansionrequired in the crown zone and the great expansion in the radially innerzone of the sidewall could not be accomplished. Therefore, the straindistribution required for the improvement of the durability could not berealized.

In practice, the particular change in configuration can be easilyobtained by ensuring the configuration of the carcass when the tiremounted on a rim is filled with 5% of the normal inner pressure on thebasis of limitations of the present invention as explained hereinafter.

The carcass configurations when tires are filled with inner pressure 5%of the normal inner pressure are defined separately on the tires of atube type to be mounted on 5° flat base rims whose bead seats engagingbead portions of the tires make approximately 5° with rotating axes ofthe tires and tires of tubeless type to be mounted on 15° drop centerrims whose bead seat make approximately 15° with rotating axes of thetires, respectively, because lengths of flanges of the rims of the twokinds are different in radial directions so that distances from therotating axes of the tires to respective reference points of the tiresare different.

With a heavy duty radial tire mounted on a rim having a bead seatinclined at a degree of 5° relative to a rotating axis of the tire,according to the invention, a carcass profile in the radialcross-sections of the tire mounted on the approved rim and filled withan inner pressure 5% of the normal inner pressure and under no loadcondition is a composite curve smoothly passing through points B, A andD, where the point A is an intersection of a carcass line C of thecarcass profile with a tangent mm' in a radial direction to the carcassline at a carcass line maximum width position and the points B and D areintersections of the carcass line C and a perpendicular pp' to a beadbase line RL. the perpendicular pp' spaced apart axially outwardly froman equatorial plane M of the tire by a distance of 0.45 times a rimwidth W corresponding to a distance between flanges of the rim, and thecarcass profile fulfills three relations, a first relation 5<240/H×u<35,where u is a distance from the point A to a point E, where the point Eis a point of contact where said tangent mm' contacts an equilibriumconfiguration curve N passing through the points B and D, and H is amaximum height of the carcass line C from the bead base line RL, asecond relation 5.0<240/H×S< 13.0, where S is a maximum distance of thecarcass line C spaced inwardly from the equilibrium configuration curveN in the radial inner zone of the sidewall, and a third relation2.0<240/H×t<10.0, where t is a maximum distance of the carcass line Cspaced outwardly from the equilibrium configuration curve N in theradial outer zone of the sidewall.

As illustrated in FIG. 1, a carcass configuration in a radially innerzone of the sidewall, located between a point n where the carcassinflated line intersects with a line perpendicular to that inflated lineextending from the tire maximum width position 6 and a bottom end pointn' where the carcass inflated line intersects with a line perpendicularto that inflated line extending from a parting point of a tire surfacefrom a flange of the rim, is either a straight line or a curved linehaving a center of curvature inside the tire when the tire is filled to5% of normal inflation pressure.

With a heavy duty radial tire mounted on a rim having a bead seatinclined at a degree of 15° relative to a rotating axis of the tire,according to the invention, a carcass profile in the radialcross-sections of the tire mounted on the approved rim and filled withan inner pressure 5% of the normal inner pressure and under no loadcondition is a composite curve smoothly passing through points B, A andD. The point A is a point of contact of a carcass line C of the carcassprofile with a tangent mm' in a radial direction to the carcass line ata carcass line maximum width position. The points B and D areintersections of the carcass line C and a perpendicular pp' to a beadbase line RL, said perpendicular pp' spaced apart axially outwardly froman equatorial plane M of the tire by a distance of 0.45 times a rimwidth W corresponding to a distance between flanges of the rim. Thecarcass profile fulfills three relations first 5<210/H×u<25, where u isa distance from the point A to a point E, where the point E is a pointof contact where said tangent mm' contacts an equilibrium configurationcurve N passing through the points B and D, and H is a maximum height ofthe carcass line C from the bead base line RL, second relation3.0<210/H×S<9.0, where S is a maximum distance of the carcass line Cspaced inwardly from the equilibrium configuration curve N in the radialinner zone of the sidewall, and third 1.0<210/H×t<5.0, where t is amaximum distance of the carcass line C spaced outwardly from theequilibrium configuration curve N in the radial outer zone of thesidewall.

The equilibrium configuration curve N is indicated by the followingequation following to the so-called "equilibrium configuration theory".##EQU1## where ψ is an angle made by a tangent on a profile line of acarcass and a line parallel to the rotating axis of the tire and locatedat a distance R from the rotating axis,

R_(E) is a distance from the rotating axis to a point E where theprofile line of the carcass has the maximum width in a direction of therotating axis, and

R_(S) is a distance from the rotating axis to a point S where a tangentto an extension of the equilibrium profile line becomes parallel to therotating axis of the tire.

An equilibrium profile line of the carcass passing through the carcassmaximum width Point E, points B and D and the tangent mm' (determined bythe standard or the like) is shown in broken lines in FIGS. 5 and 6 as areference line. In this case, the point B is located at a distance of0.15 H to 0.30 H from the rotating axis and the point D is at a distanceof 0.82 H to 0.98 H.

The distance HE, illustrated in FIG. 1 from the turn-up end of thecarcass ply is 10-35% of a maximum tire height SH measured from a beadbase line when the tire is filled to its normal inflation pressure.

FIGS. 7 and 8 illustrates carcass profiles in solid lines in radialcross-sections and equilibrium configuration curves of carcass in brokenlines which pass through points B and D and contacts tangents of thecarcass lines, when tires of the naturally equilibrium configurations ofthe prior art mounted on rims are filed with the inner pressure 5% ofthe normal inner pressure, which are tube and tubeless tires,respectively. The solid and broken lines are substantially coincidentwith each other and therefore it is clear that the tires of the priorart are designed on the basis of the equilibrium configuration curves.

Referring to FIG. 5, according to the invention with a tire using a 5°flat base rim, a carcass line passes outside the line N of theequilibrium configuration in a radially outer zone of a sidewall withina range of 2.0<240/H×t<10.0, where t is the maximum deviation from theline N of the equilibrium configuration. In the radially outer zone ofthe sidewall, moreover, in order to obtain a larger curvature, a carcassprofile maximum width point A, where a width of the carcass profile inthe direction of the rotating axis of the tire is maximum, is locatedradially outwardly of a carcass profile maximum width point E of theequilibrium configuration by a distance u between the points A and Ewithin a range of 5.0<240/H×u<35. With this arrangement, it is possibleto realize the sufficient outward expansion in the crown portion and theradially inner zones of the sidewalls and the sufficient inwarddepression in the radially outer zones of the sidewalls according to theinvention when the tire is filled with the normal inner pressure. In theradially inner zone of the sidewall, furthermore, the maximum deviations of the carcass profile from the line N of the equilibriumconfiguration is within a range of 5.0<240/H×S<13.0 according to theinvention. This feature brings about a configuration tending to approachthe equilibrium configuration when filled with the normal inner pressurein conjunction with the feature of the carcass line passing inside theequilibrium configuration, thereby improving the durability of the tire.

Referring to FIG. 6 with a tire using a 15° drop center rim, accordingto the invention, a carcass line passes outside the line N of theequilibrium configuration in a radially outer zone of a sidewall withina range of 1.0<210/H×t<5.0 where t is the maximum deviation from theline N of the equilibrium configuration. In the radial outer zone of thesidewall, moreover, in order to obtain a larger curvature, a carcassprofile maximum width point A is located radially outwardly of a carcassprofile maximum width point E of the equilibrium configuration by adistance u between the points A and E within a range of 5.0<210/H×u<25.In this manner, it is possible to realize the sufficient outwardexpansion in the crown portion and the radially inner zone of thesidewall when filled with the normal inner pressure. In the radiallyinner zone of the sidewall, moreover, the maximum deviation s of thecarcass profile from the line N of the equilibrium configuration iswithin a range of 3.0<210/H×S<9.0 according to the invention. Thisfeature brings about a configuration tending to approach the equilibriumconfiguration when filled with the normal inner pressure in conjunctionwith the feature or the carcass line passing inside the equilibriumconfiguration, thereby improving the durability of the tire.

With values of the t, s and u smaller than their minimum values, thesufficient change in configuration could not be obtained when filledwith the normal inner pressure, so that the durability could not beimproved. On the other hand, with values of the t, s and u larger thantheir maximum values, a deformation when filled with the normal innerpressure becomes excessive to increase shearing strains at ends of pliesso that the durability of the tire lowers.

With a heavy duty radial tire mounted on a rim having a bead baseengaging said bead portions, said bead seat inclined at a degree of 5°relative to a rotating axis of the tire, according to the invention, acarcass profile in the radial cross-sections of the tire mounted on theapproved rim and filled with an inner pressure 5% of the normal innerpressure and under no load condition is a composite curve smoothlypassing through points F, A and G, where the point A is a point ofcontact of a carcass line C of the carcass profile with a tangent mm' ina radial direction to the carcass line at a carcass line maximum widthposition and the points F and G are intersections of the carcass line Cand a perpendicular ll' to a bead base line RL, the perpendicular ll'spaced apart axially outwardly from an equatorial plane M of the tire bya distance of 0.5 times a rim width corresponding to a distance betweenflanges of the rim, and the carcass profile fulfills three relations, afirst relation 0<240 /H×v<3.5, where v is a maximum distance of thecarcass line C spaced outwardly of a segment of line FI connecting thepoints F and I, where the point I is an intersection of the tangent mm'and a straight line jj' which is in parallel with a rotating axis of thetire and spaced from the bead base line RL by a distance LH of 0.55times H, where H is a maximum height of the carcass line C from the beadbase line RL, a second relation 4.0<240/H×w<9.5, where w is a maximumdistance of the carcass line C spaced outwardly of an arc GI passingthrough the point G contacting and tangent to the tangent mm' at thepoint I, and a third relation 15<240/H×x<35, where x is a distancebetween the points A and I.

With a heavy duty radial tire mounted on a rim having a bead seatinclined at a degree of 15° relative to a rotating axis of the tire,according to the invention, a carcass profile in the radialcross-sections of the tire mounted on the approved rim whose and filledwith an inner pressure 5% of the normal inner pressure and under no loadcondition is a composite curve smoothly passing through points F, A andG, where the point A is a point of contact of a carcass line C of thecarcass profile and a tangent mm' in a radial direction to the carcassline at a carcass line maximum width position and the points F and G areintersections of the carcass line C and a perpendicular ll' to a beadbase line RL, the perpendicular ll' spaced apart axially outwardly froman equatorial plane M of the tire by a distance of 0.5 times a rim widthcorresponding to a distance between flanges of the rim, and the carcassprofile fulfills three relations, first 0<210/H×v<5.0, where v is amaximum distance of the carcass line C spaced outwardly of a segment ofline FI connecting the points F and I, where the point I is anintersection of the tangent mm' and a straight line jj' which is inparallel with a rotating axis of the tire and spaced from the bead baseline RL by a distance LH of 0.55 times H, where H is a maximum height ofthe carcass line C from the bead base line RL, second 2.0<210/H×w<8.0,where w is a maximum distance of the carcass line C spaced outwardly ofan arc GI passing through the point G contacting and tangent to thetangent mm' at the point I, and third 6.0<210/H×x<30.0, where x is adistance between the points A and I.

FIGS. 9 and 10 illustrate carcass lines of tires of preferableembodiments of the invention in section using 5° flat base rim and 15°drop center rim, respectively. On the other hand, FIGS. 11 and 12illustrate tires of the equilibrium configuration of the prior art thesame in size as those shown in FIGS. 9 and 10. In FIGS. 11 and 12, adifference between the carcass line of the tire of the prior art and anarc GI is small so that the arc GI substantially indicates the carcassprofile of the tire of the prior art. On the other hand, the carcassprofile is greatly deviated from a straight line FI in the zone from theradially inner area of the sidewall to a bead portion as shown in FIGS.11 and 12 illustrating tires of the prior art.

In contrast herewith, according to the embodiment of the invention acarcass line of a tire using a 5° flat base rim is deviated in theradially outer zone of the sidewall outwardly from a reference line (arcGI) indicating the carcass line of the tire of the prior art by adistance within a range of 4.0<240/H×w<9.5 as shown in FIG. 9. A carcassline of a tire using a 15° drop center rim is deviated outwardly fromthe arc GI by a distance within a range of 2.0<210/H×w<8.0 as shown inFIG. 10.

In order to deform the carcass in the radially inner zone of thesidewall selectively and greatly outwardly when filled with the normalinner pressure, it is necessary to arrange the carcass line in this zoneinside the line of the naturally equilibrium configuration. According tothe invention, therefore, the carcass line of a tire using a 5° flatbase rim in the radially inner zone of the sidewall is preferablylocated inwardly of the straight line FI by a distance v within a rangeof 0<240/H×v<3.5. The carcass line of a tire using a 15° drop center rimis preferably located inwardly of the straight line FI by a distance vwithin a range of 0<210/H×v<5.0. Moreover, with the tire using the 5°flat base rim, a carcass maximum width point A is preferably locatedradially outwardly from the standard intersection point I by a distancex within a range of 15<240/H×x<30. With the tire using the 15° dropcenter rim, a carcass maximum width point A is preferably locatedradially outwardly from the point i by a distance x within a range of6.0<210/H×x<30.0. The purpose of this feature is to obtain a curvatureof the carcass line in the radially outer zone larger than that in thetire of the prior art.

With values of the w and x smaller than their minimum values and valuesof the v larger than its maximum value, the sufficient change inconfiguration could not be obtained as described later when filled withthe normal inner pressure. On the other hand, with values of the w and xlarger than their maximum values, a deformation when filled with thenormal inner pressure becomes excessive to increase shearing strains sothat the durability of the tire rather lowers.

With a heavy duty radial tire mounted on a rim having a bead seatinclined at a degree of 5° relative to a rotating axis of the tire,according to the ivenntion, a carcass profile in the radialcross-sections of the tire mounted on the approved rim and filled withan inner pressure 5% of the normal inner pressure and under no loadcondition is a composite curve smoothly passing through points R, A andG. The point A is a point of contact of a carcass line C of the carcassprofile with a tangent mm' in a radial direction to the carcass line ata carcass line maximum width position. The point R is an intersection ofthe carcass line C and a straight line kk' in parallel with and spacedfrom a bead base line RL by a distance MH of 0.3 times a maximum heightH of the carcass line C from the bead base line RL. The point G is anintersection of the carcass line C and a perpendicular ll' to a beadbase line RL, the perpendicular ll' spaced apart axially outwardly froman equatorial plane M of the tire by a distance of 0.5 times a rim widthcorresponding to a distance between flanges of the rim. The carcassprofile fulfills three relations. A first relation is 6.0<210/H×y<11.5,where y is a maximum distance of the carcass line C from an arc IR whichpasses through the point R and contacts the said tangent mm' at a pointI, where the point I is an intersection of the tangent mm' and astraight line jj' which is in parallel with a rotating axis of the tireand spaced radially outwardly from the bead base line RL by a distanceLH 0.55 times the maximum height H of the carcass line C, a secondrelation 4.0<210/H×w<9.5, where w is a maximum distance of the carcassline C from an arc GI which passes through the point G and contacts thetangent mm' at the point I. A third relation 15<210/H×x<35, where x is aradially outward distance between the points A and I.

With a heavy duty radial tire mounted on a rim having a bead seatinclined at a degree of 15° relative to a rotating axis of the tire,according to a carcass profile in the radial cross-sections of the tiremounted on the approved rim and filled with an inner pressure 5% of thenormal inner pressure and under no load condition is a composite curvesmoothly passing through points R, A and G. The point A is a point ofcontact of a carcass line C of the carcass profile and a tangent mm' ina radial direction to the carcass line at a carcass line maximum widthposition. The point R is an intersection of the carcass line C and astraight line kk' in parallel with and spaced from a bead base line RLby a distance LH of 0.3 times a maximum height H of the carcass line Cfrom the bead base line RL. The point G is an intersection of thecarcass line C and a perpendicular ll' to a bead base line RL, theperpendicular ll' spaced apart axially outwardly from an equatorialplane M of the tire by a distance of 0.5 times a rim width correspondingto a distance between flanges of the rim. The carcass profile fulfillsthree relations, a first relation 3.0<210/H×y<8.0, where y is a maximumdistance of the carcass line C from an arc IR which passes through thepoint R and contacts the tangent mm' at a point I, where the point I isan intersection of the tangent mm' and a straight line jj' which is inparallel with a rotating axis of the tire and spaced radially outwardlyfrom the bead base line RL by a distance LH 0.55 times the maximumheight H of the carcass line C. A second relation is 2.0<210/H×w<8.0,where w is a maximum distance of the carcass line C from an arc GI whichpasses through the point G and contacts the tangent mm' at the point I.A third relation is 6.0<210/H×x<30.0, where x is a radially outwarddistance between the points A and I.

FIGS. 13 and 14 illustrate carcass lines of tires of further preferableembodiments of the invention in section using 5° flat base rim and 15°drop center rim, respectively. FIGS. 15 and 16 illustrate tires of theequilibrium configuration of the prior art of the same in size as thoseshown in FIGS. 13 and 14. In FIGS. 15 and 16, a difference between thecarcass line of the tire of the prior art and an arc GI is small so thatthe arc GI substantially indicates the carcass profile of the tire ofthe prior art. Moreover, the carcass profile is greatly deviated from astraight line IR in comparison with those shown in FIGS. 1 and 4.

In order to deform the carcass in the radially inner zone of thesidewall selectively and greatly outwardly when filled with the normalinner pressure, it is necessary to arrange the carcass line in this zoneinside an arc IR. According to the invention, therefore, the carcassline of a tire using a 5° flat base rim in the radially inner zone ofthe sidewall is preferably located inwardly of the arc IR by a distancey within a range of 6.0<210/H×y<11.5. The carcass line of a tire using a15° drop center rim is preferably located inwardly of the arc IR by adistance y within a range of 3.0<210/H×y<8.0.

In general, most failures of a tire occur at ends of a carcass or beadportions.

In order to eliminate the failures at the ends of the carcass ply,appropriate compression stresses are applied to the ends of the carcassply to prevent the failures at the ends of the carcass ply so as toimprove the durability of the bead portions.

In more detail, when the expansion f in the radially inner zone of thesidewall is caused axially outwardly by filling with the normal innerpressure, the proximity of the end e of the carcass ply within a zone of±10-20 mm is extended radially inwardly as well as axially outwardly asshown in broken lines in FIG. 17, so that the application of thecompression force to the end of the carcass ply is realized.

In order to apply an appropriate compression force, moreover, it ispreferable that a center of radius of curvature of the carcass line inthe radially inner zone of the sidewall is inside of the tire or thecarcass line is similar to a straight line.

The tensile force in the belt is increased by expanding the crown zoneor more particularly the part from an equatorial line to the ends of themaximum ground contact width when filling with the inner pressure.

The increase of the tension of the belt greatly contributes to theimprovement of the durability at the ends of the belt, because strainsoccurring between belt layers when a load is applied are mitigated toprevent separations at the ends of the belt.

In other words, referring to FIG. 18 illustrating a deformation of abelt caused by a load applied to the tire,, when an initial tensionapplied to the belt is large, a center O of the circle in a solid lineis positioned higher from a center O' of the circle in a dot-and-dashline when an initial tension applied to the belt is small. Therefore,the deformation of the belt in a deformation zone R on the groundcontact side is small, so that the shearing strains between belt layerswhose cords extend in intersecting directions are mitigated, therebyimproving the durability at ends of the belt.

The strain distribution above described is obtained by particularlylinked deformations caused when filled with the normal inner pressure toachieve the improvement of the durability at the crown portion and thebead portions.

Examples of tires according to the invention and comparative examples oftires of the prior art will be explained hereinafter.

EXAMPLE 1 OF THE INVENTION

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         240 mm                                                   ______________________________________                                    

Referring to FIG. 5, the height H is a distance from the outermostposition of the carcass to a bead base line or rim diameter line (RL)which is parallel to a rotating axis of the tire and passes through apoint on a normal outer diameter of the rim. In this case, the point onthe normal outer diameter of the rim corresponds to a point ofintersection between a surface of the rim engaging a bead base of thetire and a flange surface of the rim perpendicular to the rotating axisof the tire.

Referring to FIG. 5, tires of the Example 1 of the invention for trucksand buses were produced by way of trial, which had values S=10.0 mm,t=7.8 mm and u=23.9 mm with respect to its carcass line C determined bythe points B and D located at distances from the line RL:53.2 mm(0.22·H) and 226 mm (0.94·H), respectively.

Moreover, these steel radial tires had values, d=1.3 mm, f=6.7 mm, g=1.9mm, h=26.5 mm, c=75 mm and HE=67.2 mm referring to FIG. 1. In this case,s, t and u are within the following ranges. ##EQU2##

COMPARATIVE EXAMPLE 1

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         240 mm                                                   ______________________________________                                    

Referring to FIG. 7, tires of the Comparative Example 1 for trucks andbuses were produced for a comparison. These tires had values s=1.6 mm,t=0.3 mm and u=0.2 mm with respect to its carcass line C' determined bythe points B and D located at distances from the line RL:49.0 mm(0.20·H) and 224.2 mm (0.91·H), respectively. These steel radial tireshad the naturally equilibrium configuration exhibiting the uniformlyexpanded deformations of the prior art when filled with the normal innerpressure as shown in FIG. 3. As can be seen from the following values,the carcass lines are considerably deviated from the carcass line Caccording to the invention. ##EQU3##

EXAMPLE 2 OF THE INVENTION

    ______________________________________                                        Tire size            7.50 R 16                                                Rim size             600 GS 16                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.0 kg/cm.sup.2                                          Carcass outermost height H                                                                         178 mm                                                   ______________________________________                                    

Referring to FIG. 5, tires of the Example 2 for trucks and buses wereproduced by way of trial, which had values s=4.6 mm, t=2.8 mm and u=8.5mm with respect to its carcass line C determined by the points B and Dlocated at distances from the line RL:41.5 mm (0.23·H) and 166 mm(0.93·H), respectively. Moreover, these steel radial tires had values,d=0.8 mm, f=5.0 mm, and c=1.0 mm referring to FIG. 1.

COMPARATIVE EXAMPLE 2

    ______________________________________                                        Tire size            7.50 R 16                                                Rim size             600 GS 16                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.0 kg/cm.sup.2                                          Carcass outermost height H                                                                         178 mm                                                   ______________________________________                                    

Referring to FIG. 7, tires of the Comparative Example 2 for trucks andbuses had values s=1.2 mm, t=0 mm and u=0.5 mm with respect to itscarcass line C' determined by the points B and D located at distancesfrom the line RL:40.2 mm (0.23·H) and 161.5 mm (0.91·H), respectively.These tires were steel radial tires of the naturally equilibriumconfiguration of the prior art when filled with the normal innerpressure as shown in FIG. 3.

EXAMPLE 3 OF THE INVENTION

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         241 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Example 3 of inventionwere produced for trial, which had values s=7.0 mm, t=5.9 mm and u=16.7mm with respect to its carcass line C determined by the points B and Dlocated at distances from the line RL:50 mm (0.21·H) and 229.7 mm(0.95·H), respectively, by referring to FIG. 5 and had values, d=1.5 mm,f=5.0 mm, and e=1.8 mm referring to FIG. 1.

COMPARATIVE EXAMPLE 3

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         240                                                      ______________________________________                                    

Tires of the Comparative Example 3 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 3, and having values, s=3.0 mm, t=0.9 mm and u=2.5 mm withrespect to its carcass line C' determined by the points B and D locatedat distances from the line RL:48.7 mm (0.20·H) and 226.0 mm (0.94·H),respectively, by referring to FIG. 7.

Distributions of tensions in belts in radial cross-sections of the tiresof the Example 1 of the invention and the Comparison Example 1 of theprior art were obtained by the finite-element method, results of whichare shown in FIG. 9. The respective tires have four belt layers in theorder of first, second, third and fourth layers from the radially innerto radially outer side. The distributions of the tension of the secondand third layers are shown in FIG. 19. In this case, the distributionsof the tension were analyzed under no load when the normal innerpressure was filled.

As can be seen from FIG. 19, the circumferential tension in the tireaccording to the invention is larger than that in the tire of theComparative Examples. This holds true in the relations between theExamples 2 and 3 of the invention and the Comparative Examples 2 and 3.

Comparative tests were carried out to determine the effect of theincrease in tension of the belts on the durability of ends of the beltsby a slip angled drum test wherein a tire arranged with a slip anglerelative to a drum in contact with a tread of the tire was driven by thedrum. The tires were driven at a speed of 60 km/hr with a slip angle 3°with the normal inner pressure under twice the normal load.

As results of the test, when tires of the Examples 1, 2 and 3 of theinvention had run ran 895 km, 802 km and 840 km, slight separationsoccurred at ends of belts. On the other hand, separations occurred atends of belts when the tires of the Comparative Examples 1, 2 and 3 hadrun 630 km, 625 km and 592 km, respectively.

Moreover, these tires were tested with a drum testing machine forexamining the durability at bead portions.

These tires were driven at 60 km/hr with the normal inner pressure undertwice the normal load.

As results of the test, after the tires of the Example 1 of theinvention had run 20,000 km, any failures did not occur, but slightseparations occurred at ends of plies when the tires of the Examples 2and 3 had run 19,800 km and 19,500 km, respectively.

Separations occurred when the tires of the Comparative Examples 1, 2 and3 had run 14,500 km, 14,550 km and 15,000 km.

EXAMPLE 4 OF THE INVENTION

    ______________________________________                                        Tire size           11/70 R 22.5                                              Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             8.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        166 mm                                                    ______________________________________                                    

Steel radial tires for trucks and buses of the Example 4 of inventionwere produced for trial, which had values s=5.8 mm, t=1.7 mm and u=9.0mm with respect to its carcass line C determined by the points B and Dlocated at distances from the line RL:30.5 mm (0.18·H) and 157.2 mm(0.94·H), respectively, by referring to FIG. 6 and had values, d=1.1 mm,f=4.2 mm, g=1.7 mm, h=13.2 mm, c=41 mm and HE=19 mm referring to FIG. 2.In this case, s, t and u are within the following ranges. ##EQU4##

COMPARATIVE EXAMPLE 4

    ______________________________________                                        Tire size           11/70 R 22.5                                              Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             8.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        166 mm                                                    ______________________________________                                    

Tires of the Comparative Example 4 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, s=1.2 mm, t=0.5 mm and u=1.0 mm withrespect to its carcass line C' determined by the points B and D locatedat distances from the line RL:30.5 mm (0.18·H) and 157.2 mm (0.94·H),respectively, by referring to FIG. 8.

In this case, the carcass lines are considerably deviated from thecarcass line C according to the invention. ##EQU5##

EXAMPLE 5 OF THE INVENTION

    ______________________________________                                        Tire size              285/75 R 24.5                                          Rim size               8.25 × 24.5                                      Normal inner pressure  7.7 kg/cm.sup.2                                        Carcass outermost height H                                                                           183 mm                                                 ______________________________________                                    

Steel radial tires for trucks and buses of the Example 5 of theinvention were produced for trial, which had values s=5.0 mm, t=2.5 mmand u=9.0 mm with respect to its carcass line C determined by the pointsB and D located at distances from the line RL:38.8 mm (0.21·H) and 172.5mm (0.95·H), respectively, by referring to FIG. 6 and had values, d=2.5mm, f=7.3 mm, and g=1.8 mm referring to FIG. 2.

COMPARATIVE EXAMPLE 5

    ______________________________________                                        Tire size           285/75 R 24.5                                             Rim size            8.25 × 24.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             7.7 kg/cm.sup.2                                           Carcass outermost height H                                                                        183 mm                                                    ______________________________________                                    

Tires of the Comparative Example 5 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIGS. 3 and 4, and having values, s=1.5 mm, t=0 mm and u=0 mmwith respect to its carcass line C' determined by the points B and Dlocated at distances from the line RL:39.0 mm (0.21·H) and 172.2 mm(0.94·H), respectively, by referring to FIG. 4.

EXAMPLE 6 OF THE INVENTION

    ______________________________________                                        Tire size           11 R 22.5                                                 Rim size            8.25 × 22.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             7.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        210 mm                                                    ______________________________________                                    

Steel radial tires for trucks and buses of the Example 6 of theinvention were produced for trial, which had values s=7.0 mm, t=3.5 mmand u=12.5 mm with respect to its carcass line C determined by thepoints B and D located at distances from the line RL:40.5 mm (0.19·H)and 190 mm (0.90·H), respectively, by referring to FIG. 6 and hadvalues, d=1.2 mm, f=7.5 mm, and g=1.8 mm by referring to FIG. 2.

COMPARATIVE EXAMPLE 6

    ______________________________________                                        Tire size           11 R 22.5                                                 Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             7.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        210 mm                                                    ______________________________________                                    

Tires of the Comparative Example 6 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, s=0.8 mm, t=0.5 mm and u=1.8 mm withrespect to its carcass line C' determined by the points B and located atdistances from the line RL:40.5 mm (0.19·H) and 190.0 mm (0.90·H),respectively, by referring to FIG. 8.

Comparative tests were effected to examine the effect of the increase intension of the belts on the durability of ends of the belts by the slipangled drum test as above described.

The tires were driven at a speed of 60 km/hr with a slip angle 3° withthe normal inner pressure under twice the normal load.

As results of the test, when the tires of the Examples 4, 5 and 6 of theinvention had run 806 km, 818 km and 828 km, slight separations occurredat ends of plies. On the other hand, separations occurred at ends ofbelts when the tires of the Comparative Examples 4, 5 and 6 had run 605km, 640 km and 603 km, respectively.

Moreover, these tires were tested with the drum testing machine forexamining the durability at bead portions

These tires were driven at 60 km/hr with the normal inner pressure undertwice the normal load.

As results of the test, slight separations occurred at ends of plieswhen the tires of the Examples 4, 5 and 6 had run 19,050 km, 19,300 kmand 19,750 km, respectively.

Separations occurred when the tires of the Comparative Examples 4, 5 and6 had run 14,500 km, 15,700 km and 16,400 km.

EXAMPLE 7 OF THE INVENTION

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         240 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Example 7 of theinvention were produced for trial, which had values v=0 mm, w=7.8 mm andx=23.9 mm with respect to its carcass line C determined by the points I,F and G located at distances from the line RL:132 mm (0.55·H) and 68.5mm (0.29·H) and 221 mm (0.92·H), respectively, by referring to FIG. 9and had values, v=0 mm, w=7.8 mm, and x=23.9 mm referring to FIG. 1. Inthis case, v, w and x are within the following ranges. ##EQU6##

COMPARATIVE EXAMPLE 7

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         240 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Comparative Example 7were produced for comparison, which were steel radial tires having thenaturally equilibrium configuration when filled with normal innerpressure as shown in FIG. 3, and having values, v=4.3 mm, w=3.0 mm andx=9.3 mm with respect to its carcass line C' determined by the points I,F and G located at distances from the line RL:132 mm (0.55·H), 65.5 mm(0.27·H) and 217.5 mm (0.90·H), respectively, by referring to FIG. 11.

In this case, as can be seen from the following values, the carcasslines are considerably deviated from the carcass line C according to theinvention. ##EQU7##

EXAMPLE 8 OF THE INVENTION

    ______________________________________                                        Tire size            7.50 R 16                                                Rim size             6.00 GS 16                                                                    (5° flat base rim)                                Normal inner pressure                                                                              7.0 kg/cm.sup.2                                          Carcass outermost height H                                                                         178 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Example 8 of inventionwere produced for trial, which had values v=0 mm, w=3.4 mm and x=16.8 mmwith respect to its carcass line C determined by the points I, F and Glocated at distances from the line RL:97.9 mm (0.55·H), 55.0 mm (0.31·H)and 161.0 mm (0.9·H), respectively, by referring to FIG. 9 and hadvalues, v=0 mm, w=3.4 mm and x=16.8 mm by referring to FIG. 1.

COMPARATIVE EXAMPLE 8

    ______________________________________                                        Tire size            7.50 R 16                                                Rim size             6.00GS 16                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.0 kg/cm.sup.2                                          Carcass outermost height H                                                                         178 mm                                                   ______________________________________                                    

Tires of the Comparative Example 8 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 3, and having values, v=4.8 mm, w=0.9 mm and x=4.8 mm withrespect to its carcass line C' determined by the points I, F and Glocated at distances from the line RL:97.9 mm (0.55·H), 49.0 mm (0.28·H)and 150.0 mm (0.85·H), respectively, by referring to FIG. 11.

EXAMPLE 9 OF THE INVENTION

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         241.5 mm                                                 ______________________________________                                    

Steel radial tires for trucks and buses of the Example 9 of inventionwere produced for trial, which had values v=0 mm, w=7.5 mm and x=28.5 mmwith respect to its carcass line C determined by the points I, F and Glocated at distances from the line RL:132/9 mm (0.55·H), 57.5 mm(0.24·H) and 224 mm (0.93·H), respectively, by referring to FIG. 9 andhad values, d=1.5 mm, f=6.5 mm and g=1.8 mm by referring to FIG. 1.

COMPARATIVE EXAMPLE 9

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal. inner pressure                                                                             7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         241.5 mm                                                 ______________________________________                                    

Tires of the Comparative Example 9 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 3, and having values, v=4.5 mm, w=3.8 mm and x=3.8 mm withrespect to its carcass line C' determined by the points I, F and Glocated at distances from the line RL:132.8 mm (0.55·H), 57.5 mm(0.24·H) and 224 mm (0.93·H), respectively, by referring to FIG. 11.

Comparative tests were effected to examine the effect of the increase intension of the belts on the durability of ends of the belts by the slipangled drum test as above described.

The tires were driven at a speed of 60 km/hr with a slip angle 3° withthe normal inner pressure under twice the normal load.

As results of the test, slight separations occurred when the tires ofthe Examples 7, 8 and 9 of the invention had run 865 km. On the otherhand, separations occurred at ends of belts when the tires of theComparative Examples 7, 8 and 9 had run 630 km, 673 km and 600 km,respectively.

Moreover, these tires were tested with a drum testing machine forexamining the durability at bead portions.

These tires were driven at 60 km/hr with the normal inner pressure undertwice the normal load.

As results of the test, slight separations occurred at ends of plieswhen the tires of the Examples 7 and 8 had run 19,450 km and 19,000 km,respectively, while the tires of the Example 9 had run 20,000 km withoutcausing any failure.

As results of the test, slight separations occurred at ends of plieswhen the tires of the Examples 4, 5 and 6 had run 19,050 km, 19,300 kmand 19,750 km, respectively.

Separations occurred when the tires of the Comparative Examples 7, 8 and9 had run 14,500 km, 15,700 km and 15,000 km.

EXAMPLE 10 OF THE INVENTION

    ______________________________________                                        Tire size           11/70 R 22.5                                              Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             8.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        167.5 mm                                                  ______________________________________                                    

Steel radial tires for trucks and buses of the Example 10 of inventionwere produced for trial, which had values v=2.5 mm, w=3.0 mm and x=15.4mm with respect to its carcass line C determined by the points I, F andG located at distances from the line RL:92.1 mm (0.55·H), 44.3 mm(0.26·H) and 146 mm (0.87·H), respectively, by referring to FIG. 10 andhad values, d=1.1 mm, f=4.2 mm, g=1.7 mm, h=13.2 mm, c=41 mm and HE=19mm by referring to FIG. 2.

In this case, v, w and x are within the following ranges. ##EQU8##

COMPARATIVE EXAMPLE 10

    ______________________________________                                        Tire size           11/70 R 22.5                                              Rim size            8.25 × 22.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             8.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        166.0 mm                                                  ______________________________________                                    

Tires of the Comparative Example 10 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, v=6.3 mm, w=1.2 mm and x=2.5 mm withrespect to its carcass line C' determined by the points I, F and Glocated at distances from the line RL:91.3 mm (0.55·H), 44.0 mm (0.27·H)and 146.4 mm (0.88·H), respectively, by referring to FIG. 12.

In this case, the carcass lines are considerably deviated from thecarcass line C according to the invention. ##EQU9##

EXAMPLE 11 OF THE INVENTION

    ______________________________________                                        Tire size           285/75 R 24.5                                             Rim size            8.25 × 24.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             7.7 kg/cm.sup.2                                           Carcass outermost height H                                                                        183 mm                                                    ______________________________________                                    

Steel radial tires for trucks and buses of the Example 11 of theinvention were produced for trial, which had values v=2.0 mm, w=3.7 mmand x=18.0 mm with respect to its carcass line C determined by thepoints I, F and G located at distances from the line RL:100.7 mm(0.55·H), 49.41 mm (0.27·H) and 66.5 mm (0.91·H), respectively, byreferring to FIG. 10 and had values, d=2.5 mm, f=8.0 mm, and g=1.8 mm byreferring to FIG. 2.

COMPARATIVE EXAMPLE 11

    ______________________________________                                        Tire size           285/75 R 24.5                                             Rim size            8.25 × 24.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             7.7 kg/cm.sup.2                                           Carcass outermost height H                                                                        183 mm                                                    ______________________________________                                    

Tires of the Comparative Example 11 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, v=5.0 mm, w=0.8 mm and x=4.0 mm withrespect to its carcass line C' determined by the points I, F and Glocated at distances from the line RL:100.7 mm (0.55·H), 49.0 mm(0.27·H) and 166.8 mm (0.91·H), respectively, by referring to FIG. 12.

EXAMPLE 12 OF THE INVENTION

    ______________________________________                                        Tire size           11 R 22.5                                                 Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             7.0 kg/cm.sup.2                                           Carcass outermost distance H                                                                      210 mm                                                    ______________________________________                                    

Steel radial tires for trucks and buses of the Example 12 of theinvention were produced for trial, which had values v=2.9 mm, w=3.8 mmand x=16.7 mm with respect to its carcass line C determined by thepoints I, F and G located at distances from the line RL:115.5 mm(0.55·H), 54.5 mm (0.26·H) and 181.0 mm (0.86·H), respectively, byreferring to FIG. 10 and had values, d=1.2 mm, f=6.3 mm, and g=1.7 mm byreferring to FIG. 2.

COMPARATIVE EXAMPLE 12

    ______________________________________                                        Tire size           11 R 22.5                                                 Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             7.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        210 mm                                                    ______________________________________                                    

Tires of the Comparative Example 12 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, v=5.8 mm, w=1.2 mm and x=5.0 mm withrespect to its carcass line C' determined by the points I, F and Glocated at distances from the line RL:115.5 mm (0.55·H), 154.5 mm(0.26·H) and 180.7 mm (0.86·H), respectively, by referring to FIG. 12.

Comparative tests were effected to examine the effect of the increase intension of the belts on the durability of ends of the belts by the slipangled drum test as above described.

The tires were driven at a speed of 60 km/hr with a slip angle 3° withthe normal inner pressure under twice the normal load.

As results of the test, slight separations occurred at the ends of thebelts when the tires of the Examples 10, 11 and 12 had run 803 km, 815km and 833 km, respectively. On the other hand, separations occurred atthe ends of belts when the tires of the Comparative Examples 10, 11 and12 had run 605 km, 645 km and 592 km, respectively.

Moreover, these tires were tested with the drum testing machine forexamining the durability at bead portions.

These tires were driven at 60 km/hr with the normal inner pressure undertwice the normal load.

As results of the test, slight separations occurred at ends of plieswhen the tires of the Examples 10, 11 and 12 had run 18,500 km, 19,200km and 20,000 km, respectively.

Separations occurred when the tires of the Comparative Examples 10, 11and 12 had run 13,200 km, 16,500 km and 15,900 km.

EXAMPLE 13 OF THE INVENTION

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         242 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Example 13 of inventionwere produced for trial, which had values y=10.0 mm, w=7.8 mm and x=23.9mm with respect to its carcass line C determined by the points I, R andG located at distances from the line RL:133.1 mm (0.55·H) and 72.6 mm(0.30·H) and 220 mm (0.91·H), respectively, by referring to FIG. 13 andhad values, d=1.3 mm, f=6.7 mm, g=2.0 mm, h=27.0 mm, c=75.0 mm andHE=67.1 mm by referring to FIG. 1.

In this case, y, w and x are within the following ranges. ##EQU10##

COMPARATIVE EXAMPLE 13

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         242 mm                                                   ______________________________________                                    

Tires of the Comparative Example 13 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 3, and having values, y=4.4 mm, w=3.0 mm and x=9.3 mm withrespect to its carcass line C' determined by the points I, R and Glocated at distances from the line RL:133.1 mm (0.55·H), 72.4 mm(0.30·H) and 219 mm (0.90·H), respectively, by referring to FIG. 15.

As can be seen from the following values, the carcass lines areconsiderably deviated from the carcass line C according to theinvention. ##EQU11##

EXAMPLE 14 OF THE INVENTION

    ______________________________________                                        Tire size            7.50 R 16                                                Rim size             600 GS 16                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.0 kg/cm.sup.2                                          Carcass outermost height H                                                                         178 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Example 14 of theinvention were produced for trial, which had values y=5.5 mm, w=3.4 mmand x=16.8 mm with respect to its carcass line C determined by thepoints I, R and G located at distances from the line RL:97.9 mm(0.55·H), 53.4 mm (0.30·H) and 162.5 mm (0.91·H), respectively, byreferring to FIG. 13 and had values, d=2.8 mm, f=5.1 mm, and g=1.0 mmreferring to FIG. 1.

COMPARATIVE EXAMPLE 14

    ______________________________________                                        Tire size            7.50 R 16                                                Rim size             600 GS 16                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.0 kg/cm.sup.2                                          Carcass outermost height H                                                                         178 mm                                                   ______________________________________                                    

Tires of the Comparative Example 14 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 3, and having values, s=3.0 mm, t=0.9 mm and u=2.5 mm withrespect to its carcass line C' determined by the points I, R and Glocated at distances from the line RL:97.9 mm (0.55·H), 53.4 mm (0.30·H)and 162.5 mm (0.91·H), respectively, by referring to FIG. 15.

EXAMPLE 15 OF THE INVENTION

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         241 mm                                                   ______________________________________                                    

Steel radial tires for trucks and buses of the Example 15 of theinvention were produced for trial, which had values y=9.8 mm, w=6.5 mmand x=23.5 mm with respect to its carcass line C determined by thepoints I, R and G located at distances from the line RL:132.6 mm(0.55·H), 72.3 mm (0.30·H) and 226 mm (0.94·H), respectively, byreferring to FIG. 13 and had values, d=1.5 mm, f=5.0 mm, and g=1.8 mm byreferring to FIG. 1.

COMPARATIVE EXAMPLE 15

    ______________________________________                                        Tire size            10.00 R 20                                               Rim size             7.50 V 20                                                                     (5° flat base rim)                                Normal inner pressure                                                                              7.25 kg/cm.sup.2                                         Carcass outermost height H                                                                         241 mm                                                   ______________________________________                                    

Tires of the Comparative Example 15 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 3, and having values, y=3.6 mm, w=3.8 mm and x=3.8 mm withrespect to its carcass line C' determined by the points I, R and Glocated at distances from the line RL:132.6 mm (0.55·H), 72.0 mm (0.3·H)and 226.5 mm (0.94·H), respectively, by referring to FIG. 15.

Comparative tests were effected to examine the effect of the increase intension of the belts on the durability of ends of the belts by the slipangled drum test as above described.

The tires were driven at a speed of 60 km/hr with a slip angle 3° withthe normal inner pressure under twice the normal load.

As results of the test, slight separations occurred at ends of the beltswhen the tires of the Examples 13, 14 and 15 had run 890 km, 802 km and851 km. On the other hand, separations occurred at ends of belts whenthe tires of the Comparative Examples 13, 14 and 15 had run 585 km, 640km and 612 km, respectively,

Moreover, these tires were tested with the drum testing machine forexamining the durability at bead portions.

These tires were driven at 60 km/hr with the normal inner pressure undertwice the normal load.

As results of the test, slight separations occurred at ends of plieswhen the tires of the Examples 13 and 15 had run 18,500 km and 19,000km, respectively, while the tires of the Example 14 ran 20,000 kmwithout causing any separation.

Separations occurred when the tires of the Comparative Examples 13, 14and 15 had run 14,900 km, 16,000 km and 15,550 km.

EXAMPLE 16 OF THE INVENTION

    ______________________________________                                        Tire size           11/70 R 22.5                                              Rim size            8.25 × 22.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             8.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        168.2 mm                                                  ______________________________________                                    

Steel radial tires for trucks and buses of the Example 16 of inventionwere produced for trial, which had values y=4.8 mm, w=3.0 mm and x=15.4mm with respect to its carcass line C determined by the points I, R andG located at distances from the line RL:92.5 mm (0.55·H), 50.5 mm(0.30·H) and 148 mm (0.88·H), respectively, by referring to FIG. 14 andhad values, d=1.1 mm, f=4.2 mm, g=1.7 mm, h=13.2 mm, c=41 mm and HE=19mm by referring to FIG. 2.

In this case, y, w and x are within the following ranges. ##EQU12##

COMPARATIVE EXAMPLE 16

    ______________________________________                                        Tire size           11/70 R 22.5                                              Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             8.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        167.5 mm                                                  ______________________________________                                    

Tires of the Comparative Example 16 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, y=2.0 mm, w=1.2 mm and x=2.8 mm withrespect to its carcass line C' determined by the points I, R and Glocated at distances from the line RL:92.1 mm (0.55·H), 50.3 mm (0.3·H)and 152 mm (0.91·H), respectively, by referring to FIG. 16.

As can be seen from the following values, the carcass lines areconsiderably deviated from the carcass line C according to theinvention. ##EQU13##

EXAMPLE 17 OF THE INVENTION

    ______________________________________                                        Tire size           285/75 R 24.5                                             Rim size            8.25 × 24.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             7.7 kg/cm.sup.2                                           Carcass outermost height H                                                                        183 mm                                                    ______________________________________                                    

Steel radial tires for trucks and buses of the Example 17 of theinvention were produced for trial, which had values y=5.1 mm, w=3.7 mmand x=18.3 mm with respect to its carcass line C determined by thepoints I, R and G located at distances from the line RL:100.7 mm(0.55·H), 54.9 mm (0.30·H) and 165.5 mm (0.90·H), respectively, byreferring to FIG. 14 and had values, d=2.5 mm, f=7.3 mm, and g=1.8 mmreferring to FIG. 2.

COMPARATIVE EXAMPLE 17

    ______________________________________                                        Tire size           285/75 R 24.5                                             Rim size            8.25 × 24.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             7.7 kg/cm.sup.2                                           Carcass outermost height H                                                                        183 mm                                                    ______________________________________                                    

Tires of the Comparative Example 17 were produced for comparison, whichwere steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, y=1.9 mm, w=0.8 mm and x=4.0 mm withrespect to its carcass line C' determined by the points I, G and Rlocated at distances from the line RL:100.7 mm (0.55·H), 54.9 mm(0.30·H) and 165.1 mm (0.90·H), respectively, by referring to FIG. 16.

EXAMPLE 18 OF THE INVENTION

    ______________________________________                                        Tire size           11 R 22.5                                                 Rim size            8.25 × 22.5                                                             (15° drop center rim)                              Normal inner pressure                                                                             7.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        210 mm                                                    ______________________________________                                    

Steel radial tires for trucks and buses of the Example 18 of theinvention were produced for trial, which had values u=4.9 mm, w=3.8 mmand x=16.7 mm with respect to its carcass line C determined by thepoints I, R and G located at distances from the line RL:115.5 mm(0.55·H), 54.5 mm (0.30·H) and 181.4 mm (0.86·H), respectively, byreferring to FIG. 5 and had values, d=1.2 mm, f=7.5 mm, and g=1.7 mm byreferring to FIG. 2.

COMPARATIVE EXAMPLE 18

    ______________________________________                                        Tire size           11 R 22.5                                                 Rim size            8.25 × 22.5 (15° drop                                            center rim)                                               Normal inner pressure                                                                             7.0 kg/cm.sup.2                                           Carcass outermost height H                                                                        210 mm                                                    ______________________________________                                    

Tires of the Comparative Example 18 were produced for a comparison,which were steel radial tires for trucks and buses having the naturallyequilibrium configuration when filled with the normal inner pressure asshown in FIG. 4, and having values, y=1.8 mm, w=1.2 mm and x=4.4 mm withrespect to its carcass line C' determined by the points I, R and Glocated at distances from the line RL:115.5 mm (0.55·H), 54.5 mm(0.30·H) and 181.4 mm (0.86 H), respectively, by referring to FIG. 16.

Comparative tests were effected to examine the effect of the increase intension of the belts on the durability of ends of the belts by the slipangled drum test as above described.

The tires were driven at a speed of 60 km/hr with a slip angle 3° withthe normal inner pressure under twice the normal load.

As results of the test, slight separations occurred at the ends of thebelts when the tires of the Examples 16, 17 and 18 had run 865 km, 802km and 845 km. On the other hand, separations occurred at ends of beltswhen the tires of the Comparative Examples 16, 17 and 18 had run 620 km,629 km and 598 km, respectively.

Moreover, these tires were tested with the drum testing machine forexamining the durability at bead portions.

These tires were driven at 60 km/hr with the normal inner pressure undertwice the normal load.

As results of the test, slight separations occurred at ends of plieswhen the tires of the Examples 16 and 17 had run 18,800 km and 18,550km, respectively, while the tires of the Example 18 ran 20,000 kmwithout causing any failure.

Separations occurred when the tires of the Comparative Examples 16, 17and 18 had run 14,200 km, 15,750 km and 16,050 km.

As can be seen from the above explanation, the heavy duty radial tireaccording to the invention is considerably improved in durability atbead portions and ends of the belt.

It is further understood by those skilled in the art that the foregoingdescription is that of preferred embodiments of the disclosed tires andthat various changes and modifications may be made in the inventionwithout departing from the spirit and scope thereof.

What is claimed is:
 1. In a heavy duty radial tire including at least one radial carcass extending from one bead portion to the other bead portion and using inextensible cords and a belt arranged outwardly of the radial carcass for reinforcing a tread of the tire, the improvement comprising; an outer profile of the tire in radial cross-sections mounted on an approved rim, said rim having a width which is not wider than that of a design rim and under no load condition during filling of said tire inner pressure from 5% to 100% of a normal inner pressure, said outer profile of the tire comprising a first profile portion expanding during filling radially outwardly in a tread zone from one end of said tread through a crown center to the other end of said tread, the ends of said tread also expanding outwardly, a second profile portion depressing axially inwardly of the tire at least in a part of a radially outer zone of a sidewall from said one end of said tread to a tire maximum width position when said tire is filled with the normal inner pressure, and a third profile portion expanding during filling axially outwardly of the tire in a radially inner zone of said sidewall from said tire maximum width position to a parting point of the sidewall from the rim flange when said tire is filled with the normal inner pressure thereby properly distributing strains occurring in the tire when inflated to a normal inner pressure, said tire mounted on a rim having a bead seat engaging said bead portions of said tire, said bead seat being inclined at a degree of 5° relative to a rotating axis of the tire, wherein a carcass profile in the radial cross-sections of the tire mounted on the approved rim and filled with an inner pressure 5% of the normal inner pressure and under no load condition is a composite curve smoothly passing through points F, A and G, where the point A is a point of contact of a carcass line C of the carcass profile with a tangent mm' in a radial direction to the carcass line at a carcass line maximum width position and the points F and G are intersections of the carcass line C and a perpendicular ll' to a bead base line RL, said perpendicular ll' spaced apart axially outwardly from an aquatorial plane M of the tire by a distance of 0.5 times a rim width corresponding to a distance between flanges of the rim, and said carcass profile fulfills three relations in millimeters, a first relation 0<240/H×v<3.5, where v is a maximum distance of the carcass line C spaced outwardly of a segment of line FI connecting the points F and I, where the point I is an intersection of the tangent mm' and a straight line jj' which is in parallel with a rotating axis of the tire and spaced from the bead base line RL by a distance LH of 0.55 times H, where H is a maximum height of the carcass line C from the bead base line RL, a second relation 4.0<240/H×w<9.5, whereby w is a maximum distance of the carcass line C spaced outwardly of an arc GI passing through the point G contacting and tangent to the tangent mm' at the point I, and a third relation 15<240/H×x<35, where x is a distance between the points A and I.
 2. In a heavy duty radial tire including at least one radial carcass extending from one bead portion to the other bead portion and using inextensible cords and a belt arranged outwardly of the radial carcass for reinforcing a tread of the tire, the improvement comprising; an outer profile of the tire in radial cross-sections mounted on an approved rim, said rim having a width which is not wider than that of a design rim and under no load condition during filling of said tire inner pressure from 5% to 100% of a normal inner pressure, said outer profile of the tire comprising a first profile portion expanding during filling radially outwardly in a tread zone from one end of said tread through a crown center to the other end of said tread, the ends of said tread also expanding outwardly, a second profile portion depressing axially inwardly of the tire at least in a part of a radially outer zone of a sidewall from said one end of said tread to a tire maximum width position when said tire is filled with the normal inner pressure, and a third profile portion expanding during filling axially outwardly of the tire in a radially inner zone of said sidewall from said tire maximum width position to a parting point of the sidewall from the rim flange when said tire is filled with the normal inner pressure thereby properly distributing strains occurring in the tire when inflated to a normal inner pressure, said tire mounted on a rim having a bead seat engaging said bead portions of said tire, said bead seat being inclined at a degree of 15° relative to a rotating axis of the tire, wherein a carcass profile in the radial cross-sections of the tire mounted on the approved rim and filled with an inner pressure 5% of the normal inner pressure and under no load condition is a composite curve smoothly passing through points F, A and G, where the point A is a point of contact of a carcass line C of the carcass profile with a tangent mm' in a radial direction to the carcass line at a carcass line maximum width position and the points F and G are intersections of the carcass line C and a perpendicular ll' to a bead base line RL, said perpendicular ll' spaced apart axially outwardly from an equatorial plane M of the tire by a distance of 0.5 times a rim width corresponding to a distance between flanges of the rim, and said carcass profile fulfills three relations in millimeters, a first relation 2<210/H ×v<5.0, where v is a maximum distance of the carcass line C spaced outwardly of a segment of line FI connecting the points F and I, where the point I is an intersection of the tangent mm' and a straight line jj' which is in parallel with a rotating axis of the tire and spaced from the bead base line RL by a distance LH of 0.55 times H, where H is a maximum height of the carcass line C from the bead base line RL, a second relation 2.0<210/H×w<8.0, where w is a maximum distance of the carcass line C spaced outwardly of an arc GI passing through the point G contacting and tangent to the tangent mm' at the point I, and a third relation 6.0<210/H×X<30.0, where x is a distance between the points A and I. 